Energy transfer model for the derivative nonlinear schrodinger equations on the torus

Abstract

We consider the nonlinear derivative Schrödinger equation with a quintic nonlinearity, on the one dimensional torus. We exhibit that the nonlinear dynamic properties of the particular solution consisting of four frequency modes initially excited, whose frequencies include the resonant clusters and phase matched resonant interactions of nonlinearities. The proof is based on the analysis of resonant dynamics via a finite dimensional ordinary differential system.